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list of abstracts - Faculdade de Ciências
list of abstracts - Faculdade de Ciências

Light Scattering Group - University of Hertfordshire
Light Scattering Group - University of Hertfordshire

Notes
Notes

Final Exam Study Guide File
Final Exam Study Guide File

...  Methods of separation (distillation, filtration, chromatography)  Law of conservation of energy, converting to different forms  Energy unit conversion problems  Temperature scales, conversions (°C ↔ K)  Heat calculations – calorimeter, q = mcT 4 – Atoms and Elements  Democritus  Dalton’s at ...
The Electromagnetic Field
The Electromagnetic Field

ATAR Year 12 sample course outline - SCSA
ATAR Year 12 sample course outline - SCSA

Extra Dimensions, no kidding
Extra Dimensions, no kidding

Physics 311A Special Relativity
Physics 311A Special Relativity

Why is this a problem?
Why is this a problem?

... This worked at longer wavelengths but deviates badly at short ones. This problem became known as the ultraviolet catastrophe and was one of the many effects classical physics couldn’t explain. ...
Solution
Solution

Quantum Theory of Light, PY4T02 Problem Set 2 Paul Eastham
Quantum Theory of Light, PY4T02 Problem Set 2 Paul Eastham

... 2. (a) Consider the single-mode electric field operator Ex = E0 sin(kz)(a + a† ). Calculate the expectation value and variance of the electric field when this mode is in a number state |ni. (b) What is the characteristic scale of the electric field fluctuations for a mode of volume 1µm3 at a wavelen ...
Special Relativity and Fields Homework problem, due 13th October
Special Relativity and Fields Homework problem, due 13th October

Basic_Equations
Basic_Equations

Earlier examination problems
Earlier examination problems

A 1
A 1

Homework 1 Solutions
Homework 1 Solutions

... Homework 1 Solutions Problem 1: Electromagnetic Field The idea behind these problems is to “re-derive” some of the known results in electromagnetism using the classical field theory approach, i.e., with the Lagrangian ...
Basics of electrodynamics
Basics of electrodynamics

3 Maxwell`s equations and material equations
3 Maxwell`s equations and material equations

The Differential Geometry and Physical Basis for the Application of
The Differential Geometry and Physical Basis for the Application of

Professor Emeritus, University of Canterbury Yevgeny Lifshitz
Professor Emeritus, University of Canterbury Yevgeny Lifshitz

Derivation of EMHD Equations
Derivation of EMHD Equations

PHY-105: Equations of Stellar Structure
PHY-105: Equations of Stellar Structure

... also a function or r) – see previous handout for more discussion of opacity. These 4 equations have 7 unknowns (at a given r): P , Mr , Lr , T , ρ, ǫ, κ. So in general we require expressions for P , κ, and ǫ in terms of ρ, T , and the compositions. These can be complicated, but for example if we ass ...
Eddington`s Theory of Gravity and Its Progeny
Eddington`s Theory of Gravity and Its Progeny

The Observational Status of the Cosmological Standard Model
The Observational Status of the Cosmological Standard Model

CLASSICAL MODEL OF A CHARGED PARTICLE WITH ANGULAR
CLASSICAL MODEL OF A CHARGED PARTICLE WITH ANGULAR

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Kaluza–Klein theory

In physics, Kaluza–Klein theory (KK theory) is a unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the usual four of space and time. It is considered to be an important precursor to string theory.The five-dimensional theory was developed in three steps. The original hypothesis came from Theodor Kaluza, who sent his results to Einstein in 1919, and published them in 1921. Kaluza's theory was a purely classical extension of general relativity to five dimensions. The 5-dimensional metric has 15 components. Ten components are identified with the 4-dimensional spacetime metric, 4 components with the electromagnetic vector potential, and one component with an unidentified scalar field sometimes called the ""radion"" or the ""dilaton"". Correspondingly, the 5-dimensional Einstein equations yield the 4-dimensional Einstein field equations, the Maxwell equations for the electromagnetic field, and an equation for the scalar field. Kaluza also introduced the hypothesis known as the ""cylinder condition"", that no component of the 5-dimensional metric depends on the fifth dimension. Without this assumption, the field equations of 5-dimensional relativity are enormously more complex. Standard 4-dimensional physics seems to manifest the cylinder condition. Kaluza also set the scalar field equal to a constant, in which case standard general relativity and electrodynamics are recovered identically.In 1926, Oskar Klein gave Kaluza's classical 5-dimensional theory a quantum interpretation, to accord with the then-recent discoveries of Heisenberg and Schrödinger. Klein introduced the hypothesis that the fifth dimension was curled up and microscopic, to explain the cylinder condition. Klein also calculated a scale for the fifth dimension based on the quantum of charge.It wasn't until the 1940s that the classical theory was completed, and the full field equations including the scalar field were obtained by three independent research groups:Thiry, working in France on his dissertation under Lichnerowicz; Jordan, Ludwig, and Müller in Germany, with critical input from Pauli and Fierz; and Scherrer working alone in Switzerland. Jordan's work led to the scalar-tensor theory of Brans & Dicke; Brans and Dicke were apparently unaware of Thiry or Scherrer. The full Kaluza equations under the cylinder condition are quite complex, and most English-language reviews as well as the English translations of Thiry contain some errors. The complete Kaluza equations were recently evaluated using tensor algebra software.
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